Funny enough, pretty consistently for the first ~300 years of the Empire, and then intermittently for the next ~300 years, the Romans still regarded themselves as meaningfully being a republic. All the time, when you read Roman legislation, it’s phrased in terms of “By the consensus of the people and Senate”. In the earliest ~200 years of the Empire, the formalities of taking legislature through the Senate were still strong, and could even credibly block the Emperor.

Of course, the bigger issue is that the Senate was actually the least democratic form of the old republic; the Senate survived, while the democratically-functioning tribunes and assemblies of the people that the Senate constantly attempted to neuter finally lost most of their power.